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Fertility and Its Measurement
Stan Becker, PhD
Bloomberg School of Public Health
Section A
Indicators of Fertility Based
on Vital Statistics
Definitions
Š Fecundity—Physiological capacity to
conceive
Š Infecundity (sterility)—Lack of the capacity
to conceive
– Primary sterility—Never able to produce
a child
– Secondary sterility—Sterility after one or
more children have been born
Continued
4
Definitions
Š Fecundability—Probability that a woman
will conceive during a menstrual cycle
Š Fertility (natality)—Manifestation of
fecundity
Š Infertility—Inability to bear a live birth
Š Natural fertility—Fertility in the absence of
deliberate parity-specific control
Continued
5
Definitions
Š Reproductivity—Extent to which a group is
replacing its own numbers by natural
processes
Š Gravidity—Number of pregnancies a
woman has had
Š Parity—Number of children born alive to a
woman
Continued
6
Definitions
Š Birth interval—Time between successive
live births
Š Pregnancy interval—Time between
successive pregnancies of a woman
7
Crude Birth Rate (CBR)
Š Let B
=
Š Let P
=
Š Let W15-44 =
Number of births
Mid-year population
Number of women of
reproductive ages
Continued
8
Crude Birth Rate (CBR)
Š Crude Birth Rate—Number of births per
1,000 population
B
= ∗ 1000
P
W15 − 44
=
∗
∗ 1000
W15 - 44
P
B
9
Exercise
Crude Birth Rate (CBR)
Š Use the following data to calculate the CBR
per 1,000
Island of Mauritius, 1985
Total Births: 18,247
Total female population: 491,310
Total male population: 493,900
You have 15 seconds to calculate the answer. You
may pause the presentation if you need more time.
Source: U.N. Demographic Yearbook, 1986
10
Exercise Answer
Crude Birth Rate (CBR)
Š The correct answer is as follows:
– 18.5 births per 1,000 population
Island of Mauritius, 1985
Total Births: 18,247
Total female population: 491,310
Total male population: 493,900
11
Crude Birth Rate (CBR)
Š Crude birth rates can be standardized using
the direct or the indirect method
Š Example: Direct (DSBR) and indirect (ISBR)
standardization of the Island of Mauritius
(I.M.) 1985 crude birth rate using Mali's
1987 data as standard
12
Direct Standardization of Birth
Rate for Mauritius Island
(Study)
(Standard)
Age group Rates I.M. per Population
1000
Mali
15-19
18
725719
20-24
58
574357
25-29
57
536226
30-34
36
443702
35-39
19
379184
40-44
6
325824
Total
2985012
Total number of births, Mali:
Total number of births, I.M.:
CBR Mali:
CBR I.M.
Expected
number of
births, I.M.
13063
33313
30565
15973
7204
1955
102073
375117
18247
48.7
18.5
Source: U.N. Demographic Yearbook, 1986, 1992, 1996
13
Indirect Standardization of
Birth Rate for Mauritius Island
Age group
15-19
20-24
25-29
30-34
35-39
40-44
Total
(Standard)
(Study)
Rates Mali Population
per 1000
I.M.
79
105764
159
109914
171
94576
140
81144
107
60063
50
45825
497286
Total number of births, Mali:
Total number of births, I.M.:
CBR Mali:
CBR I.M.
Expected
number of
births, I.M.
8355
17476
16172
11360
6427
2291
62082
375117
18247
48.7
18.5
Source: U.N. Demographic Yearbook, 1986, 1992, 1996
14
Expected births in I.M.
I.M.
DSBR
=
∗ CBR
Mali
Actual births in Mali
102073
=
∗ 48.7 = 13 .3
375117
Observed births in I.M.
Mali
I.M.
ISBR
=
∗ CBR
Expected births in I.M .
18247
=
∗ 48 .7 = 14 .3
62082
CBR I.M. = 18.5
Source: U.N. Demographic Yearbook, 1986, 1996
15
General Fertility Rate (GFR)
Š General Fertility Rate—Number of births
per 1,000 women of reproductive ages
=
B
W15 - 44
∗ 1000
GFR ≈ 4 ∗ CBR
16
Exercise
General Fertility Rate (GFR)
Š Use the following data to calculate the GFR
per 1,000 women aged 15–44:
Island of Mauritius, 1985
Age Group
15-19
20-24
25-29
30-34
35-39
40-44
Women
52 013
54 307
46 990
40 211
30 401
23 496
Total births: 18 247
You have 15 seconds to calculate the answer. You may pause the
presentation if you need more time.
Source: U.N. Demographic Yearbook, 1986
Continued
17
Exercise
General Fertility Rate (GFR)
Š The correct answer is:
– 73.7 births per 1,000 women aged
15-44
Island of Mauritius, 1985
Age Group
15-19
20-24
25-29
30-34
35-39
40-44
Women
52 013
54 307
46 990
40 211
30 401
23 496
Total births: 18 247
18
Age-Specific Fertility
Rate (ASFR)
Š Let Ba = Number of births to women of
age (group) “a”
Wa = Number of women of age
(group) “a”
n = Number of years in age group
19
Age-Specific Fertility
Rate (ASFR[a, n])
Š ASFR(a, n)—Number of births per 1,000
women of a specific age (group)
Ba
= Fa =
∗ 1000
Wa
Š If n = 1 , then write ASFR(a)
Š Example: ASFR Poland 1984
20
Rate (per
thousand)
Age-Specific Fertility Rates
Poland, 1984
200
150
100
50
0
15-19 20-24 25-29 30-34 35-39 40-44 45-49
Age Group
21
Exercise
Age-Specific Fertility Rate (ASFR[a, n])
Š Use the following data to calculate the
ASFR per 1,000 for women age 20–24 and
25–29
Island of Mauritius, 1985
Age Group
of Mother
15-19
20-24
25-29
30-34
35-39
40-44
Women
52 013
54 307
46 990
40 211
30 401
23 496
Source: U.N. Demographic Yearbook, 1986
Births
1884
6371
5362
2901
1170
268
22
Exercise Answer
Age-Specific Fertility Rate (ASFR)
Š The correct answers are:
– ASFR(20,5) = 117.3 births per 1,000 women 20–24
– ASFR(25,5) = 114.1 births per 1,000 women 25–29
Island of Mauritius, 1985
Age Group
of Mother
15-19
20-24
25-29
30-34
35-39
40-44
Women
52 013
54 307
46 990
40 211
30 401
23 496
Births
1884
6371
5362
2901
1170
268
23
Total Fertility Rate (TFR)
Š Total Fertility Rate—Number of children a
woman will have if she lives through all the
reproductive ages and follows the agespecific fertility rates of a given time period
(usually one year)
Continued
24
Total Fertility Rate (TFR)
Š For single-year age groups
44 B
a ∗ 1000 = ∑ ASFR(a) = ∑ F
TFR = ∑
a
W
a = 15 a
Š For five-year age groups
40- 44
B
a ∗ 1000 = 5 *
TFR = 5 ∗ ∑
ASFR(a,5)
∑
a=15−19 W
a=15-19
a
40− 44
Continued
25
Total Fertility Rate (TFR)
Š Example: ASFR and TFR—Poland, 1984
Age group
Ba
15-19
43807
20-24
257872
25-29
236088
30-34
115566
35-39
38450
40-44
6627
Wa ASFR
1230396 35.60
1390077 185.51
1653183 142.81
1608925 71.83
1241967 30.96
941963
7.04
473.74
TFR= (5 * 473.74) / 1000 = 2.4
26
Exercise
Total Fertility Rate (TFR)
Š Use the following data to calculate the TFR
per 1,000
Island of Mauritius, 1985
Age Group
of Mother
15–19
20–24
25–29
30–34
35–39
40–44
Women
52,013
54,307
46,990
40,211
30,401
23,496
Source: U.N. Demographic Yearbook, 1986
Births
1,884
6,371
5,362
2,901
1,170
268
27
Exercise Answer
Total Fertility Rate (TFR)
Š The correct answer is as follows:
– TFR = 1.9 children per woman
Island of Mauritius, 1985
Age Group
of Mother
15–19
20–24
25–29
30–34
35–39
40–44
Women
52,013
54,307
46,990
40,211
30,401
23,496
Births
1,884
6,371
5,362
2,901
1,170
268
28
Mean of Age of Childbearing
Š For single-year groups
∑ (a + 1 2 ) Fa
44
_
a=
a =15
44
∑ Fa
a =15
Š For five-year age groups
_
a=
∑ (a + 2 . 5 ) Fa
∑ Fa
29
Variance of Age of Childbearing
2
_⎞
⎛
⎜
⎟
a
a
Fa
−
∑
⎜
⎟
a = 15 ⎝
2
⎠
s =
44
∑ Fa
44
a = 15
30
Exercise
Mean and Variance of Age of Childbearing
Š Use the following data to calculate the
mean and variance of age of childbearing
Island of Mauritius, 1985
Age Group
of Mother
15Ğ19
20Ğ24
25Ğ29
30Ğ34
35Ğ39
40Ğ44
Women
52,013
54,307
46,990
40,211
30,401
23,496
Source: U.N. Demographic Yearbook, 1986
Births
1,884
6,371
5,362
2,901
1,170
268
31
Exercise Answer
Mean and Variance of Age of Childbearing
Š The correct answers are as follows:
– Mean age of childbearing = 27.9 years
– Variance of age of childbearing = 38.2
years
Island of Mauritius, 1985
Age Group
of Mother
15Ğ19
20Ğ24
25Ğ29
30Ğ34
35Ğ39
40Ğ44
Women
52,013
54,307
46,990
40,211
30,401
23,496
Births
1,884
6,371
5,362
2,901
1,170
268
32
Mean and Median Age of
Mothers
Š Mean:
β
1
(a + ) ∗ Ba
∑
2
a =α
∑ Ba
Median x such that:
x
∑ Ba
a =15
=
0
.
5
44
∑ Ba
a =15
Š Ba = Number of births to women age a
33
Exercise
Mean and Median Age of Mothers
Š Use the following data to calculate the
mean and median age of mothers
Island of Mauritius, 1985
Age Group
of Mother
15–19
20–24
25–29
30–34
35–39
40–44
Women
52,013
54,307
46,990
40,211
30,401
23,496
Source: U.N. Demographic Yearbook, 1986
Births
1,884
6,371
5,362
2,901
1,170
268
34
Exercise Answer
Mean and Median Age of Mothers
Š The correct answers are as follows:
– Mean age of mothers = 26.9 years
– Median age of mothers = 24.7 years
Island of Mauritius, 1985
Age Group
of Mother
15Ğ19
20Ğ24
25Ğ29
30Ğ34
35Ğ39
40Ğ44
Women
52,013
54,307
46,990
40,211
30,401
23,496
Births
1,884
6,371
5,362
2,901
1,170
268
35
Parity
Š Mean
I=max( i)
Mi
∑
i =1
Median x such that:
x
∑ mi
i =1
= 0 .5
Š Mi = Proportion of women at or above parity
i
Š mi = Proportion of women at parity i
36
Marital Fertility Rate (MFR)
Š Let Bm
= Number of marital births
Bu
= Number of non-marital births
Wm15–44 = Number of married women
of age 15–44
Wu15–44 = Number of unmarried
women of age 15–44
37
General Marital Fertility
Rate (GMFR)
Š General Marital Fertility Rate—Number of
births per 1,000 married women of
reproductive ages
=
B
m
W15- 44
∗ 1000
38
Marital Fertility Rate (MFR)
Š Marital Fertility Rate—Number of marital
births per 1,000 married women of
reproductive ages
Bm
= m ∗1000
W15-44
39
“Out-of-Wedlock” (Non-Marital)
Fertility Rate
Š “Out-of-Wedlock” (Non-Marital) Fertility
Rate—Number of non-marital births per
1,000 unmarried women of reproductive
ages
Bu
= u ∗1000
W15-44
40
Some Relationships
B
Bu
Bm
+
≠
u
m
W15-44 W15-44 W15-44
Š But
m
15-44
u
15-44
W
Bm W
Bu
B
∗
+
∗
=
m
u
W15-44 W15-44
W15-44 W15-44
W15-44
41
Age-Specific Marital
Fertility Rate (ASMFR)
Š Let Bma = Number of marital births to
women of age group “a”
Wma = Number of married women in
age group “a”
Bm(d) = Number of marital births to
women married for “d” years
Wm(d) = Number of women married for
“d” years
Continued
42
Age-Specific Marital
Fertility Rate (ASMFR)
Š Age-Specific Marital Fertility Rate—Number
of marital births per 1,000 married women
of age (group) “a”
Bmla
=
∗1000
m
W
a
43
Duration (of Marriage)—
Specific Fertility Rate (DSFR)
Š DSFR—Number of marital births per 1,000
women who have been married for
duration “d”
Bl(d)
=
∗ 1000
m
W (d)
44
Order-Specific Fertility
Rate (OSFR)
Š Let Bi
Bia
Wa
W15-44
= Number of births of order “i”,
i>0
= Number of order “i” births to
women in age group “a”
= Number of women in age
group “a”
= Number of women of age
15–44 (or 15–49)
Continued
45
Order-Specific Fertility
Rate (OSFR)
Š Order-Specific Fertility Rate—Number of
order “i” births per 1,000 women of
reproductive ages
=
i
B
W15 - 44
∗ 1000
Š Example: OSFR Poland 1984
46
30
20
10
th
+
10
9t
h
8t
h
7t
h
6t
h
5t
h
4t
h
3r
d
d
2n
t
0
1s
Rate (per
thousand)
Order-Specific Fertility Rates
Poland, 1984
Birth Order
47
Exercise
Order-Specific Fertility Rate (OSFR)
Š Use the following data to calculate the
OSFR for birth orders 1 and 3
Island of Mauritius, 1985
Age Group
of Mother
15Ğ19
20Ğ24
25Ğ29
30Ğ34
35Ğ39
40Ğ44
Number of Birth Order
Women
1
3
52,013
1,521
40
54,307
3,317
678
46,990
1,638
1,132
40,211
496
665
30,401
142
215
23,496
24
30
Source: U.N. Demographic Yearbook, 1986
48
Exercise Answer
Order-Specific Fertility Rate (OSFR)
Š The correct answers are as follows:
– OSFR(1) = 28.8 births of order 1 per
1,000 women 15–44
– OSFR(3) = 11.2 births of order 3 per
1,000 women 15–44
Island of Mauritius, 1985
Age Group
of Mother
15–19
20–24
25–29
30–34
35–39
40–44
Number of Birth Order
Women
1
3
52,013
1,521
40
54,307
3,317
678
46,990
1,638
1,132
40,211
496
665
30,401
142
215
23,496
24
30
49
Age-Order Specific Fertility
Rate (AOSFR [a,I])
Š AOSFR(a,i)—Number of order “i” births per
1,000 women of age (group) “a”
i
Ba
=
∗ 1000
Wa
Š Example: AOSFR Poland 1984
50
Age-Order Specific Fertility Rates
1st birth
Poland 1984
2nd
3rd
4th +
120
100
80
60
40
20
0
-20
20-24 25-29 30-34 35-39 40-44
45+
Age
51
Exercise
Age-Order Specific Fertility Rate (AOSFR)
Š Use the following data to calculate the AOSFR
for birth order 3 in age group 25–29
Island of Mauritius, 1985
Age Group
of Mother
15Ğ19
20Ğ24
25Ğ29
30Ğ34
35Ğ39
40Ğ44
Birth order
Women
1
3
52,013 1,521
40
54,307 3,317
678
46,990 1,638
1,132
40,211
496
665
30,401
142
215
23,496
24
30
Source: U.N. Demographic Yearbook, 1986
52
Exercise Answer
Age-Order Specific Fertility Rate (AOSFR)
Š The correct answer is as follows:
– AOSFR = 24.1 births of order 3 per
1,000 women 25–29
Island of Mauritius, 1985
Age Group
of Mother
15–19
20–24
25–29
30–34
35–39
40–44
Birth order
Women
1
3
52,013 1,521
40
54,307 3,317
678
46,990 1,638
1,132
40,211
496
665
30,401
142
215
23,496
24
30
53
Age-Order Specific Fertility
Rate (AOSFR[a,i])
Š Note:
∞
∑ AOSFR (a, i ) = ASFR ( a )
i =1
44
Wa
= O SFR(i)
∑ AOSFR (a, i ) ∗
W15 - 44
a =15
54
Cumulative Order Specific
Birth Rate (COSFR[i,a])
Š Cumulative up to age “a”
Š COSFR(i,a)—Total number of order “i”
births per 1,000 women of age (group) less
than or equal to “a”
a
= ∑ AOSFR(i, x)
x=0
55
Birth Probability
Š Let Bi
Wi-1
= Number of births of order “i”, i>0,
in year “t”
= Number of women of parity
“i-1” at beginning of year “t”
56
Birth Probability, BP(i)
Š Birth Probability—Probability of having an
“ith” order birth in a given year for women
who already have “i-1” births
=
i
B
W
i-1
57
Birth Probability
Š May be age-specific as well
Š Birth probabilities are the most sensitive
indicators of temporal change in the pace
of childbearing
58
Paternal Fertility Rate
Š Let B
= Number of births
M15-54 = Number of men of age 15–54
59
General Fertility Rate of
Men (GFRm)
Š General Fertility Rate of Men—Number of
births per 1,000 men age 15 to 54
=
B
M15 - 54
∗ 1000
60
Summary
Š Fertility data are collected from vital
statistics, censuses, or surveys
Š Vital statistics principally provide birth
statistics
Š Many indicators have been developed to
understand and explain the fertility
patterns in populations based on vital
statistics
61
Section B
Indicators of Reproduction Based on
Vital Statistics
Gross Reproduction Rate (GRR)
Š Let Bf = Number of female births
Bm+f = Number of male and female
births, i.e., all births
Continued
63
Gross Reproduction Rate (GRR)
Š Gross Reproduction Rate—Number of
daughters expected to be born alive to a
hypothetical cohort of women (usually
1,000) if no one dies during childbearing
years and if the same schedule of agespecific rates is applied throughout the
childbearing years
Continued
64
Gross Reproduction Rate (GRR)
GRR
=
∑
ASFR
f
B (a)
(a) ∗ m + f
B
(a)
GRR = TFR ∗ (Proportion of female births)
Š If the sex ratio at birth is assumed constant
across ages of women
65
Exercise
Gross Reproduction Rate (GRR)
Š Use the following data to calculate the GRR
United States, 1990
Age
Group of
Mother
15-19
20-24
25-29
30-34
35-39
40-44
Births
Women Total
Males
8 651
522
267
9 345
094
560
10 617 1277
653
10 986
886
454
10 061
318
163
8 924
49
25
Numbers are in 1,000s
You have 15 seconds to calculate the answer. You
may pause the presentation if you need more time.
Sources: U.S. Census 1990 and Vital Statistics of the U.S. Vol. I
66
Exercise Answer
Gross Reproduction Rate (GRR)
Š The correct answer for the gross
reproduction rate is as follows:
– 1.01 daughters per woman
United States, 1990
Age
Group of
Mother
15-19
20-24
25-29
30-34
35-39
40-44
Births
Women Total
Males
8 651
522
267
9 345
094
560
10 617 1277
653
10 986
886
454
10 061
318
163
8 924
49
25
Numbers are in 1,000s
67
Net Reproduction Rate (NRR)
Š Let Lfa = Life table person-years lived
by women in age group “a”
l0 = Radix of life table
Bf = Number of female births
Bm+f = Number of male and female
births
Continued
68
Net Reproduction Rate (NRR)
Š Net Reproduction Rate—Average number
of daughters expected to be born alive to a
hypothetical cohort of women if the same
schedule of age-specific fertility and
mortality rates applied throughout the
childbearing years
Continued
69
Net Reproduction Rate (NRR)
Š For single-year age groups
NRR = ∑ ASFR ∗
f
1 a
f
l0
f
L
B
∗ m+ f
B
f
L
5 a
Bf
∗ m+ f
B
Š For five-year age groups
NRR = ∑ ASFR ∗
f
l0
70
Exercise
Net Reproduction Rate (NRR)
Š Use the following data to calculate the NRR
United States, 1990
Age
Group of
Mother
15-19
20-24
25-29
30-34
35-39
40-44
Births
Women Total
Males
8 651
522
267
9 345
094
560
10 617 1277
653
10 986
886
454
10 061
318
163
8 924
49
25
Numbers are in 1,000s
Sources: U.S. Census 1990 and Vital Statistics of the U.S. Vol. I
71
Exercise Answer
Net Reproduction Rate (NRR)
Š The correct answer for the NRR is as follows:
– 1.00 daughter per woman
United States, 1990
Age
Group of
Mother
15-19
20-24
25-29
30-34
35-39
40-44
Stationary
Births
Population
Women Total
Males
5Lx
8 651
522
267
493 629
9 345
094
560
492 399
10 617 1277
653
490 989
10 986
886
454
489 203
10 061
318
163
486 812
8 924
49
25
483 465
Numbers are in 1,000s
72
Net Reproduction Rate (NRR)
NRR
_
≈ l ( a ) ∗ GRR
Š Where l( a) = Life table probability of
surviving beyond a
a = mean age of childbearing
usually 20< a < 30
73
Live Births and Fertility Rates:
United States, 1920–1988
Source: U.S. Department of Health and Human Services, Monthly Vital
Statistics Report, Vol. 39, No. 4, Supplement, August 15, 1990
74
Completed Fertility Rates for
Birth Cohorts of Women
Source: U.S. Bureau of the Census, Current Population Reports, Series
P-25, No. 381, tables A-1 and A-2
75
Reproductivity
Š Reproductivity is usually studied in terms of
mothers and daughters because of the
following reasons:
– The fecund period for females is shorter
than it is for males
– Characteristics such as age are much
more likely to be known for the mothers
of illegitimate babies than for their
fathers
76
Summary
Š Reproductivity data are collected from vital
statistics
Š Many indicators have been developed to
understand and explain reproductivity
patterns in populations
77
Section C
Indicators of Fertility Based on
Censuses and Surveys
Child-Woman Ratio (CWR)
Š Child-Woman Ratio—Number of children
zero to four years old relative to number of
women of reproductive ages
Continued
79
Child-Woman Ratio (CWR)
P0 − 4
CWR =
∗ 1000
W15 − 44
Š Where P0-4 = Mid-year population of
persons age 0-4 years
W15-44 = Number of women of
reproductive ages
80
Exercise
Child-Woman Ratio (CWR)
Š Use the following data to calculate the
CWR
Household population composition
by age and sex, Kenya 1998
Age group
0-4
…
15-19
20-24
25-29
30-34
35-39
40-44
Male Female
268873 256705
Total
525578
189272
130899
116747
100827
88445
67218
381340
289723
258951
200555
191866
135550
192067
158825
142204
99727
103421
68332
Source: Demographic and Health Survey, Kenya 1998
81
Exercise Answer
Child-Woman Ratio (CWR)
Š The correct answer is as follows:
– 687.4 children 0-4 per 1,000
women 15-44
Household population composition
by age and sex, Kenya 1998
Age group
0-4
…
15-19
20-24
25-29
30-34
35-39
40-44
Male Female
268873 256705
Total
525578
189272
130899
116747
100827
88445
67218
381340
289723
258951
200555
191866
135550
192067
158825
142204
99727
103421
68332
82
Children Ever Born (CEB)
Š Children Ever Born—Total number of
children a woman has ever given birth to
Š The survival status of the children is not
considered here
Š Almost all censuses tabulate mean CEB by
marital status and by age of the mother
83
Parity Progression Ratios
(PPR[i])
Š Let N = Random variable for number
of births
mi = Proportion of women of parity “i”
Mi = Proportion of women at or
above parity “i”
Continued
84
Parity Progression Ratios
(PPR[i])
Š Parity Progression Ratios—Probability that
a woman has an (i+1st) birth given that
she already has had “i” births
= ai
Mi + 1
=
Mi
= Prob (N ≥ i + 1 N ≥ i)
85
Exercise
Parity Progression Ratios (PPR)
Š Given the following percentages of women at
parity “i” for women 45-49 in 1995 in Colombia,
calculate PPR(2)
Parity
0
1
2
3
4
5+
Percentage
9.2
7.5
13.9
18.6
15.6
35.2
Source: Demographic and Health Survey, Colombia 1995
86
Exercise Answer
Parity Progression Ratios (PPR)
Š The correct answer for the PPR(2) is as
follows:
– 0.83 (i.e., there is an 83% chance that a
woman 45–49 has a second birth given she
already has had a first birth)
Parity
0
1
2
3
4
5+
Percentage
9.2
7.5
13.9
18.6
15.6
35.2
87
Parity Progression Ratios (PPR)
Š Note: a0 = Prob (ever give birth)
1-a0 = Prob (never have a birth)
M0 = 1
Š ai need not decrease with increasing I
Š Mi does decrease
88
Proportion of Women of Parity
i(mi)
Š Is an unconditional probability
= Mi - Mi+1
= Prob (N ≥ i) - Prob (N ≥ i + 1)
= a0 ∗ a1 ∗ ... ∗ ai-1 ∗ (1 − ai )
Continued
89
Proportion of Women of Parity
i(mi)
Š Given the following percentages of women at
parity “i” for women 45–49 in 1995 in Colombia,
verify the relationships indicated on the previous
slide
Parity
0
1
2
3
4
5+
Percentage
9.2
7.5
13.9
18.6
15.6
35.2
Source: Demographic and Health Survey, Colombia 1995
90
Mean Parity
=
max(i)
∑M
i=1
i
=
max(i)
∑ i∗m
i=1
i
91
Exercise
Mean Parity
Š Given the following percentages of women at parity
“i” for women 45–49 in 1995 in Colombia, calculate
the mean parity using both formulas on the previous
slide (assume that women at parity 10+ are on
average at parity 11)
Parity
0
1
2
3
4
5
Percentage
9.2
7.5
13.9
18.6
15.6
10.1
Parity Percentage
6
7
8
9
10+
Source: Demographic and Health Survey, Colombia 1995
8.0
5.9
3.2
3.2
4.8
92
Exercise Answer
Mean Parity
Š The correct answer is as follows:
– Mean parity = 4.01
Parity
0
1
2
3
4
5
Percentage
9.2
7.5
13.9
18.6
15.6
10.1
Parity Percentage
6
7
8
9
10+
8.0
5.9
3.2
3.2
4.8
93
Estimation of GFR from Census
Data on Ratio of Children to Women
Š Let P0-4
= Enumerated number of
children under 5
W15-44 = Enumerated number of
women of age 15–44
W20-49 = Enumerated number of
women of age 20–49
Continued
94
Estimation of GFR from Census
Data on Ratio of Children to Women
Š Also let l0 = Radix of life table
nLa = Life table person-years
lived between the ages “a”
and “a+n” (female life table)
Continued
95
Estimation of GFR from Census
Data on Ratio of Children to Women
P0- 4 ∗
GFRest =
l0
L
5 0
W15− 44 + W20 − 49
∗
2
L
30 L 20 + 30 L15
2
30 15
Continued
96
Estimation of GFR from Census
Data on Ratio of Children to Women
Š Note:
– Assumes that a life table is available
– Estimated GFR may be used in the
absence of birth statistics to compare
fertility levels in various areas
Continued
97
Estimation of GFR from Census
Data on Ratio of Children to Women
Š The life table survivorship functions are
inverted in order to estimate the number of
persons at the mid-point of the preceding
five-year period
Š A lexis diagram makes it easier to
understand this calculation
98
Summary
Š Fertility data are collected from vital
statistics, censuses, or surveys
Continued
99
Summary
Š Censuses provide the following:
– Data on births and fertility
– Statistics on children by family status of
the parents
– Population data on fertility-related
variables
– Population bases for calculating various
types of fertility measures
Continued
100
Summary
Š Surveys provide the following:
– Same type of data as censuses
– Additional detailed data on special
aspects of fertility, including number
and timing of births, marriages,
pregnancies, birth intervals, and birth
interval components
Continued
101
Summary
Š Many indicators have been developed to
understand and explain the fertility
patterns in populations
102
Section D
Relationship among Indicators,
Indicators and Models of Birth
Intervals, and Fertility Models
Relations among Indicators
Š At age 50:
max(i)
∑ COSFR(i,50 )
i =1
= Completed cohort
fertility rate
= Mean CEB
max(i)
= ∑ Mi
i =1
Continued
104
Relations among Indicators
max(i)
∑
i=1
OSFR ( i ) =
=
max (i )
Bi
∑
i = 1 W 15 − 44
B
W 15 − 44
= GFR
105
Pregnancy Histories and
Birth Histories
Š Data needed
– Age or birth date of woman
– Dates of pregnancy terminations
– Type of termination (live birth or not)
Continued
106
Pregnancy Histories and
Birth Histories
Š Two ways of collecting data
– Forward, i.e., from first to last birth
– Backward, i.e., from last to first birth
Continued
107
Pregnancy Histories and
Birth Histories
Š Problems
– Dating of events
– Forgetting events
– Age misreporting
Continued
108
Age 35
Cohort fertility (births per 1000
women) calculated from survey
data for forward and backward
questionnaires by five-year age
groups and five-year periods
before the survey
Bangladesh, 1984
Legend:
253
277 30
332
317
274
269
241
110
58
112
313
277
xx: Forward
xx: Backward
84
20
77
15
89
10
278
88
5
Years before the survey
311 25
258 20
100 15
0
109
Birth Interval Measures
and Models
Š Let NS = Time from previous pregnancy
outcome to resumption of
ovulation (postpartum nonsusceptibility subinterval)
Š For first order births use dates of marriage
or beginning of sexual relations
Continued
110
Birth Interval Measures
and Models
Š Also let C = Time from resumption of
ovulation to next conception
(conception-wait subinterval)
G = Time from conception to next
pregnancy outcome
(gestational subinterval)
W = Waiting time due to non-live
births
111
Pregnancy and Live
Birth Intervals
Š Pregnancy interval
– PI = Interval between two pregnancies
= NS + C + G
Š Live birth interval
– LBI = Interval between two live births
= PI + W
112
Observed Birth Intervals
Š
Š
Š
Š
Closed intervals
Left censored intervals
Right censored intervals
Life table methods can be used to
incorporate the different intervals and
calculate median birth interval lengths
113
Birth Interval
Š Note:
– Mean birth interval for women is
different from mean birth interval for
births in a given time period
– The latter is shorter
114
Birth Interval
Mathematical relationships
Š In populations with nothing changing
Let p = Fecundability (assumed fixed)
e = Effectiveness of contraception
u = Proportion using contraception
s = Non-susceptible period (constant)
115
Mean Birth Interval
Mean birth interval
1
=
+s
( p (1 - ue) )
1
= Fertility rate for
Mean B irth Interval
fecund women
116
Mean Conception-Wait
Subinterval (MC)
Š Mean Conception-Wait Subinterval—Mean time it
takes to get pregnant under natural fertility
Š Constant fecundability
2
MC = 1 ∗ p + 2(1 - p)p + 3(1 - p) p + ...
1
=
p
p = Monthly probability of conception
(assumed fixed in time and for all
women)
117
Heterogeneous Fecundability
Š Probability of conception in month “k”
Š “p” is assumed to vary between women
with distribution “f(p)”
=
1
∫0
k -1
pq
f(p) dp
– Where q = 1-p
118
Probability of Conceiving
In Month “k” Given No Conception Before Then
= 1-
1 qk f(1 - q) dq
∫0
1 qk -1 f(1 - q) dq
∫0
Š Note
– Here the probability of conception
decreases over time
– This has important implications for the
study of infertility
119
Fertility Models
Coale and Trussell
Š Let r(a) = Observed fertility schedule at
age “a”
n(a) = Natural fertility pattern at age “a”
M = Level of fertility (estimated)
m = Degree to which fertility control
is practiced (estimated)
v(a) = Estimated from U.N.
Demographic Yearbook 1965;
data for 43 fertility schedules
Continued
120
Fertility Models
Coale and Trussell
r (a )
(m ∗ v(a))
=M∗e
n( a )
121
Fertility Models
Bongaarts
Š Bongaarts model of intermediate fertility variables
Let Cm = Index of marriage
Cc = Index of contraception
Ca = Index of induced abortion
Ci = Index of post-partum infecundability
K = Estimated total natural fertility
rate (15.3 [Bongaarts 1982])
Š Each “C” varies between 0.0 and 1.0
Continued
122
Fertility Models
Bongaarts
Š Methods of estimation of each “C” are
provided by Bongaarts (1982)
TFR = C m ∗ C c ∗ C a ∗ C i ∗ K
123
Summary
Š Information on women's fertility can be
obtained by asking them to report their
pregnancy and birth histories
Š Indicators and models have been
developed to understand and explain the
fertility patterns in populations
124